SL(n, R)-Toda black holes

We consider D-dimensional Einstein gravity coupled to (n − 1) U(1) vector fields and (n  −  2) dilatonic scalars. We find that for some appropriate exponential dilaton couplings of the field strengths, the equations of motion for the static charged ansatz can be reduced to a set of one-dimensional SL(n,R) Toda equations. This allows us to obtain a general class of explicit black holes with mass and (n − 1) independent charges. The near-horizon geometry in the extremal limit is AdS2 × SD−2. The n = 2 case gives the Reissner–Nordstrøm solution, and the n = 3 example includes the Kaluza–Klein dyon. We study the global structure and the black hole thermodynamics and obtain the universal entropy product formula. We also discuss the characteristics of extremal multi-charge black holes that have positive, zero or negative binding energies. (paper)